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Tri Vi Dang Columbia University Corporate Finance Fall 2011 Final Exam Please read the following instructions carefully. This exam consists of four questions. Please answer all questions. You can obtain a maximum of 70 points. You have 75 minutes for working on the questions. Do not spend too much time on a single question. Please take the number of points as a rough indicator for the minutes you work on each of the (sub-) questions. This exam is an open book exam. This means you can use all materials (textbook, lecture notes, your own notes, etc.). All types of calculators are allowed. The usage of laptops and any sorts of electronic communication devices is not allowed. Good luck! 1 Question 1 [16 points] There is an economy with three dates {t=0, 1, 2}. Consider the following relationship between a private equity firm and the portfolio company CFA (Cash Free Agency) Inc. The portfolio company has a product that generates the following cash flow. At t=1, the demand can be high or low with equal probability. If demand is high (low) the cash flow is CF1H=600 (CF1L=400). At t=2, the demand can also be high or low. If demand was high at t=1, then a high demand at t=2 arises with probability 0.7. If demand was low at t=1, then a high demand at t=2 arises with probability 0.3. If demand is high (low) at t=2 then CF2H=600 (CF2L=200). All agents are risk neural. The interest rate is r=0%. (a) Draw the event and decision tree. [3p] (b) What is the market price (expected value) of CFA Inc. at t=0? [3p] Now suppose at t=0 CFA Inc. can invest in a technology that improves the product. The investment costs are $400 which is to be financed by the private equity firm. The improved technology has the following effect. In the high demand state the demand for the product doubles at t=1 and t=2. In the low demand state it has no effect. (c) Should CFA Inc. invest in the new technology at t=0? [4p] Now consider the following contingent finance plan. The private equity firm has committed to give $400 but at t=0 it will only give $200. Then the private equity firm and CFA Inc. will negotiate about the remaining $200 at=1. Suppose investing $200 at t=0, only doubles demand in state H at t=1 but has no effect in the low demand state (i.e. CF1H=1200 and CF1L=400) at t=1 and no effect on demand at t=2. Only if CFA Inc. invests an additional $200 at=1, then this doubles demand in the high state at t=2 (i.e. CF2H=1200 and CF2L=200). (d) What strategy maximizes the value of CFA Inc. and what is the maximal firm value? [4p] (e) Do you observe such kind of contingent financing rules in real venture capital deals between the venture capitalist and a portfolio company? [2p] 2 Question 2 [24 points] Consider an economy with three dates {t=0, 1, 2}. At t=2 there are three possible states {L, M, H} which arise with the following probabilities: prob(L)=0.3, prob(M)=0.4 and prob(H)=0.3. A start up firm that produces an application for mobile internet access has assets in place that generate an output (profit) of $20 in state L, $40 in state M and $130 in state H at t=2. At t=1, the firm can implement another project. The implementation costs are $X and the new project delivers an output of $100 in state L, $100 in state M, and $120 in state H at t=2. The firm wants to sell equity to a venture capitalist to finance the new project. Both the entrepreneur of the start up firm and the venture capitalist are risk neutral. They maximize their expected payoff. The risk free rate is r=0. For questions (a) to (e), assume the investment cost is X=85. (a) What is the t=0 value of the firm (i) without and (ii) with the project? [2p] (b) What percentage of equity does the entrepreneur sell so as to raise the investment cost at t=1? [4p] Now suppose prior to selling equity the entrepreneur privately learns the true state of t=2 at t=1. (c) At t=1 does he sell equity in all three states? [3p] (d) What is the t=1 value of the firm if equity is sold at t=1? [4p] (e) What fraction of shares does the venture capitalist demand if he invests at t=1? [3p] (f) Determine the set of investment costs {X} such that there is venture capital finance in all states? [8p] 3 Question 3 [14 points] An investor wants to acquire a firm and is analyzing the financials of the firm. Its balance sheet and income information are given as follows. Figures are in $ million. Balance Sheet Assets Cash and cash equivalents Short term marketable securities Inventories Long term marketable securities Goodwill Liabilities 100 Current liabilities 30 40 Non-current liabilities 20 10 80 40 Income information Net Sales: $100 Cost of Sales (% of net sales): R&D (% of net sales): General costs (% of net sales): Tax rate: 60% 3% 7% 30% (a) What is the book equity of the firm? [1p] (b) Determine the Quick ratio of the firm. [3p] (c) Determine the gross margin, operating income and net income of the firm. [6p] The investor wants to use some simple financial multiples to obtain a rough indicator for the value of the firm. Firms competing in the same industry have a Market-to-Book (M/B) ratio of 2 and a Price-Earnings (P/E)-ratio of 8. (d) Using the current earnings of the firm and the PE ratio, what is the suggested value of the firm? What is the value of the firm using the M/B multiple approach? [4p] 4 Question 4 [16 points] Are the following statements true or false? Please give a (very) brief explanation. (a) A limited partnership agreement is a legal document that guides a private equity partnership. The document is only binding if it is approved by the Security Exchange Commission. [2p] (b) A limited partner in a private equity arrangement is the person who makes investment decisions and provides knowhow to portfolio companies. [2p] (c) A leverage buyout (LBO) occurs if a private equity firm issues equity to buy all debt of the target firm. [2p] (d) The three main components of a financial statement are balance sheet, income statement and cash flow statement. Only publicly traded companies are required to provide an income statement. [2p] (e) Book equity is defined as total assets minus total liabilities. Therefore, the market value of equity (i.e. share price times number of shares outstanding) is always larger than book equity. [2p] (f) A DCF (discounted cash flow) valuation model uses historical accounting information as inputs to calculate the fundamental value of a firm. [2p] (g) Inputs for a DCF valuation models are projected future free cash flow and depends on subjective expectations. [2p] (h) A main task of an equity analyst is to conduct business, market and financial analysis and then make stock investment recommendations. [2p] 5 Tri Vi Dang Columbia University Corporate Finance Fall 2012 Final Exam Please read the following instructions carefully. This exam consists of four questions. Please answer all questions. You can obtain a maximum of 70 points. You have 75 minutes for working on the questions. Do not spend too much time on a single question. Please take the number of points as a rough indicator for the minutes you work on each of the (sub-) questions. This exam is an open book exam. This means you can use all materials (textbook, lecture notes, your own notes, etc.). Scientific calculators are allowed. The usage of laptops and any sorts of electronic communication devices is not allowed. Good luck! 1 Question 1 [22 points] Consider an economy with three dates {t=0, 1, 2}. A start up firm that produces an application for mobile internet access has assets in place that generate an output (profit) of either $40 in state L or $200 in state H at t=2. Both states are equally likely. At t=1, the firm can implement another project. The implementation costs are $120 and the new project delivers an output of $130 in state L and $140 in state H at t=2. The firm wants to issue equity to a venture capitalist to finance the new project. Both the entrepreneur of the start up firm and the venture capitalist are risk neutral. They maximize their expected payoff. The risk free rate is r=0. (a) What is the t=0 value of the firm (i) without and (ii) with the project? [2p] (b) What percentage of equity does the venture capitalist demand for providing $120 at t=1? [3p] Now suppose prior to selling equity the entrepreneur privately obtains a signal about the true state of t=2 at t=1. For questions (c) to (e), assume the signal is perfect, i.e. the entrepreneur knows with probability one the true state. (c) At t=1 does he sell equity in both states? [3p] (d) What fraction of shares does the venture capitalist demand if he invests at t=1? [3p] (e) What is the t=1 value of the firm if equity is sold at t=1? [2p] Suppose the entrepreneur sees a high signal. But with probability p the signal is wrong, i.e. the true state is L. Suppose the venture capitalist demands an equity share as given in (b). (f) Suppose p=0.2 (i.e. the signal is correct with 80% probability). Does the entrepreneur issue equity at t=1? [6p] (g) Suppose p=0.5. Does the entrepreneur issue equity at t=1? [3p] 2 Question 2 [20 points] There is an economy with three dates {t=0, 1, 2}. Consider the following relationship between a private equity firm and the portfolio company CFA (Cash Free Agency) Inc. The portfolio company has a product that generates the following cash flow. At t=1, the demand can be high or low with equal probability. If demand is high (low) the cash flow is CF1H=600 (CF1L=200). At t=2, the demand can also be high or low. If demand is high at t=1, then a high demand at t=2 arises with probability 0.8 and CF2H=800. If demand is low at t=2 then CF2L=400. If demand is low at t=1, then a high demand at t=2 arises with probability 0.3 and CF2H=400. If demand is low at t=2 then CF2L=200. The interest rate is r=0%. (a) Draw the event and decision tree. [3p] (b) What is the market value (expected value) of CFA Inc. at t=0? [3p] Now suppose at t=0 CFA Inc. can invest in a technology that improves the product of the firm. The investment costs are $240. The improved technology has the following effect. In the low demand state at t=1 and t=2 more consumers are now willing to buy and the demand for the product doubles. In the high demand state it has no effect. (c) Should CFA Inc. invest in the new technology at t=0? What is the market value of CFA? [6p] Now suppose the private equity firm advises CFA to split the investment. If CFA invests $120 at t=0, it doubles demand in state L at t=1 but has no effect on demand at t=2. At t=1, if CFA invests $120, this doubles demand in the low state at t=2. (d) What is the optimal investment strategy and the associated market value? [8p] 3 Question 3 [12 points] Consider a VC fund which is set up for ten years with $100 million committed capital by limited partners. The fund has a management fee of 2% per year and carried interest of 80-20. Suppose at t=10 the final value (liquidation value) of the fund is $X. (a) What is the investment capital of the fund? [1p] For questions (b) to (e), X=140 million. (b) What is the payoff of the limited partner? [2p] (c) What is the payoff of the general partner (excluding fees)? [1p] For all subsequent questions, suppose there is also a hurdle rate of 10%. (d) What is the payoff of the limited partner? [3p] (e) What is the payoff of the general partner (excluding fees)? [1p] Given the above compensation structure, suppose the LP wants to have a (total) return on committed capital of 100%. (f) What is the required final value X of the fund? [4p] 4 Question 4 [16 points] Are the following statements true or false? A (very) brief explanation is required. (a) A private equity distressed fund typically invests in penny stocks. [2p] (b) A general partner (GP) in a private equity partnership prefers to have a hurdle rate since this increases the probability that the GP gets more cash flow. [2p] (c) A limited partner in a private equity partnership benefits from a catch-up. [2p] (d) A typical characteristic of a leverage buyout is when the financial sponsor (i.e. general partner of a buyout fund) holds more than half of the high yield debt that is issued to finance the buyout transaction. [2p] (e) Preferred stocks in the context of venture capital investments have voting rights. [2p] (f) The market for corporate control can mitigate the agency costs of free cash flow. [2p] (g) A main task of a strategy consultant is to conduct competitive analyses of firms. A main task of a financial analyst is to conduct valuations of firms. So he does not care about competitive analysis. [2p] (h) The stock price of a firm exhibits features of a bubble if the book value of the firm is much higher than its market value. [2p] 5